Table of contents

CONTENTS § 1. Eckmann-Hilton duality in homotopical topology § 2. Functors in the category of topological spaces § 3. Duality of functors § 4. Duality of functors in some other categories § 5. Pibrations and cofibrations § 6. On adjoint functors in the sense of D. Kan References

CONTENTS Introduction Chapter I. Auxiliary results § 1. An integral transform § 2. Generalized Faber polynomials § 3. Asymptotic approximation by polynomials § 4. A boundary value problem Chapter II. Asymptotic properties of orthogonal polynomials § 1. Extremal properties and asymptotic behaviour of the leading coefficient § 2. Asymptotic formulae § 3. An estimate of an orthogonal polynomial inside the domain § 4. A second derivation of the estimates inside the domain § 5. Polynomials orthogonal on a circle Chapter III. Fourier series in orthogonal polynomials § 1. Conditions for convergence inside the domain § 2. The rate of convergence inside the domain § 3. Convergence in the closed domain § 4. Representation of analytic functions under smoothness conditions on the contour and weight Chapter IV. Some results on the Steklov problem § 1. The Steklov problem in the theory of orthogonal polynomials § 2. Boundedness conditions and estimates of the growth of polynomials orthogonal on a contour § 3. Asymptotic properties of polynomials orthogonal on a contour when the weight function becomes infinite at isolated points § 4. Asymptotic properties of polynomials orthogonal on a contour when the weight function has isolated zeros § 5. Example References

CONTENTS Introduction § 1. Scales of Banach spaces § 2. Normal embeddings of spaces and of their duals § 3. Normal scale of spaces. Related spaces § 4. Interpolation properties. Minimal and maximal scales § 5. The Hölder scale § 6. The Marcinkiewicz scale § 7. Analytic scales § 8. Spaces of means § 9. Hilbert scales Addendum: Yu. I. Petunin. A non-linear problem in the theory of scales of Banach spaces References